Active-gel Theory for Multicellular Migration in the Extra-cellular Matrix
Ram Adar (Collège de France)
We formulate an active-gel theory for multicellular migration in the extracellular
matrix (ECM). The cells are modeled as an active, polar solvent, and the
ECM as a viscoelastic solid. Our theory enables to analyze the dynamic reciprocity
between the migrating cells and their environment in terms of distinct relative forces
and alignment mechanisms. We analyze the linear stability of polar cells migrating
homogeneously in the ECM. Our theory predicts that, as a consequence of cell-matrix
alignment, contractile cells migrate homogeneously for small wave vectors, while
sufficiently extensile cells migrate in domains. Homogeneous cell migration of both
extensile and contractile cells may be unstable for larger wave vectors, due to active
forces and the alignment of cells with their concentration gradient. These mechanisms
are stabilized by cellular alignment to the migration flow and matrix stiffness. They
are expected to be suppressed entirely for rigid matrices with elastic moduli of order
10 kPa. Our theory should be useful in analyzing multicellular migration and ECM
patterning at the mesoscopic scale.